Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 649-655.

• Articles • Previous Articles     Next Articles

Characterizations of Pairwise Stratifiable Spaces

 LI Ke-Dian   

  1. Department of Mathematics, Zhangzhou Normal University, Fujian Zhangzhou 363000
  • Received:2008-11-13 Revised:2009-12-28 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    国家自然科学基金(10571151, 10671173)和福建省自然科学基金(2006J0228, 2008F5066)资助

Abstract:

In this paper, we give some characterizations of pairwise stratifiable spaces by means of pairwise g-functions and semi-continuous functions.
It is established that: a space  (X, τ1τ2)  is pairwise stratifiable  if and only if for each f  ∈ τi - LSC(X),  one assigns an  h(f) ∈τi -LSC(X)∩τj - USC(X) such that.

(1)   0≤ h(f)≤ f and 0<h(f)(x)(x) whenever f(x)>0 .

(2)    h(f)≤ h(f') whenever f≤ f' .

Key words: Pairwise stratifiable spaces, Bitopological spaces, Pairwise monotonically space, Upper semi-continuous maps, Lower semi-continuous maps

CLC Number: 

  • 54E20
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